A General Constrained Adaptive Filtering (GCAF) algorithm is proposed via constructing a general and adaptive loss function to find out a solution of constraint optimizing problem. By selecting appropriate parameters, the GCAF algorithm can be utilized to approximate different adaptive algorithms and has higher performance than its approximated algorithms. The steady state mean squared-deviation of GCAF algorithm is derived and analyzed. Also, its complexity is presented. Simulation results demonstrated that the performance of devised GCAF method can outperform most of typically adaptive algorithms by choosing optimal parameters.